It is well known that the sample covariance is not an efficient estimator of the covariance of a bivariate normal vector. We extend this result to elliptical distributions and we propose a simple explicit estimator, which is efficient in the normal case and which outperforms the sample...

The comedianCOM(X, Y) of random variablesX,Yis a median based robust alternative to the covariance ofXofY. For the bivariate normal case it is known thatCOM(X, Y), standardized by the median absolute deviations ofXandY, is a symmetric, strictly increasing and continuous function of the...

It is well-known that the univariate generalized Pareto distributions (GPD) are characterized by their peaks-over-threshold (POT) stability. We extend this result to multivariate GPDs. It is also shown that this POT stability is asymptotically shared by distributions which are in a certain...

Bivariate generalized Pareto distributions (GPs) with uniform margins are introduced and elementary properties such as peaks-over-threshold (POT) stability are discussed. A unified parameterization with parameter [theta][set membership, variant][0,1] of the GPs is provided by their canonical...

It is assumed that observations among an iid sample falling into certain subsets of the sample space cannot be observed directly, but only through their frequencies. Bounds for the corresponding loss of information are established, which are based on the Hellinger distance between the empirical...

Pickands coordinates were introduced as a crucial tool for the investigation of bivariate extreme value models. We extend their definition to arbitrary dimensions and, thus, we can generalize many known results for bivariate extreme value and generalized Pareto models to higher dimensions and...

Let (U,V) be a random vector with U[less-than-or-equals, slant]0, V[less-than-or-equals, slant]0. The random variables Z=V/(U+V), C=U+V are the Pickands coordinates of (U,V). They are a useful tool for the investigation of the tail behavior in bivariate peaks-over-threshold models in extreme...

De Haan and Pereira (2006) [6] provided models for spatial extremes in the case of stationarity, which depend on just one parameter [beta]0 measuring tail dependence, and they proposed different estimators for this parameter. We supplement this framework by establishing local asymptotic...